Question

Mr. Mahajan and his wife are both school teachers and earn Rs. 20900 and Rs. 18700 per month respectively. Find the ratio of Mr. Mahajan’s income to his wife’s income.

Answer 1

Hint: The value of two quantities is given and their ratios can be calculated as:
\[a:b = \dfrac{a}{b}\]
The fraction is reduced so that there are no common factors between the numerator and denominator to obtain the ratio between the two quantities

Complete step-by-step answer:
Let Mr. Mahajan’s income per month be x
x = Rs. 20900
and his wife’s income per month be y
y = Rs. 18700
Ratio of x is to y can be given as:
x : y
and this ratio in terms of fraction can be written as:
\[x:y = \dfrac{x}{y}\] ___________ (1)
Substituting the values, we get:
\[
  \dfrac{x}{y} = \dfrac{{20900}}{{18700}} \\
  \dfrac{x}{y} = \dfrac{{19}}{{17}} \\
 \] [ Simplifying ]
From (1):
\[
  x:y = \dfrac{x}{y} \\
  x:y = \dfrac{{19}}{{17}} \\
 \]
x : y = 19 : 17.
Therefore, the ratio of Mr. Mahajan’s income to his wife’s income is 19 : 17

Note: Ratios are always unit less and to achieve this the numerator and denominator have the same units that get canceled out later on.
a : b is pronounced / called as ‘a is to b’. The first term is called as antecedent whereas the second is known as consequent.
Additional information: Ratio is the comparison between the two similar quantities and is denoted by ‘ : ‘ symbol. The order of the terms while writing ratio needs consideration 🡪 The quantity with respect to which the ratio is taken should be in the denominator